The qubit information logic theory for understanding multi-qubit entanglement and designing exotic entangled states

• URL: http://arxiv.org/abs/2402.15699v1
• Date: Sat, 24 Feb 2024 03:21:05 GMT
• Title: The qubit information logic theory for understanding multi-qubit entanglement and designing exotic entangled states
• Authors: Zixuan Hu and Sabre Kais
• Abstract summary: We develop a "qubit information logic" (QIL) theory that uses the "qubit information equation" (QIE) and logic to describe the correlation behaviors of multi-qubit entanglement. The QIL directly describes the correlation of each possible pair of qubits and how the correlation changes when other qubits are measured.
• Score: 3.716663957642983
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a "qubit information logic" (QIL) theory that uses the "qubit information equation" (QIE) and logic to describe the correlation behaviors of multi-qubit entanglement. Introducing the "global information status" and "local information availability", the QIL gives an alternative and natural interpretation of the "spooky action" and the quantum no-communication theorem. Compared to the conventional entropy-based entanglement theories, the QIL directly describes the correlation of each possible pair of qubits and how the correlation changes when other qubits are measured. This makes the QIL more advantageous in describing the correlation properties of multi-qubit entanglement, which is illustrated by studying the dormant entanglement phenomenon. The QIL theory's usefulness is further demonstrated by designing an exotic quantum state where two qubits can be entangled but not correlated in any arbitrary basis. Overall the QIL provides an alternative and intuitive understanding of multi-qubit entanglement that is, compared to the conventional theories, directly focused on the correlation behaviors between qubits and thus more suitable for designing exotic quantum states that may be used in quantum algorithms.

Related papers

• Uncertainty relations in terms of generalized entropies derived from information diagrams [0.0]
  Inequalities between entropies and the index of coincidence form a long-standing direction of researches in classical information theory. This paper is devoted to entropic uncertainty relations derived from information diagrams.
  arXiv  Detail & Related papers  (2023-05-29T10:41:28Z)
• A Quantum Algorithm for Computing All Diagnoses of a Switching Circuit [73.70667578066775]
  Faults are by nature while most man-made systems, and especially computers, work deterministically. This paper provides such a connecting via quantum information theory which is an intuitive approach as quantum physics obeys probability laws.
  arXiv  Detail & Related papers  (2022-09-08T17:55:30Z)
• Cone-Restricted Information Theory [5.148939336441987]
  We show which results in quantum information theory rely upon the positive semidefinite cone and which can be generalized. We present parallel results for the extended conditional min-entropy. In doing so, we extend the notion of k-superpositive channels to superchannels.
  arXiv  Detail & Related papers  (2022-06-09T06:27:48Z)
• Entropic Accord: A new measure in the quantum correlation hierarchy [0.5039813366558306]
  We show a new measure of quantum correlations which we call entropic accord that fits between entanglement and discord. We study two-qubit states which shows the relationship between the three entropic quantities.
  arXiv  Detail & Related papers  (2022-05-13T07:16:50Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Shannon theory beyond quantum: information content of a source [68.8204255655161]
  We extend the definition of information content to operational probabilistic theories. We prove relevant properties as the subadditivity, and the relation between purity and information content of a state.
  arXiv  Detail & Related papers  (2021-12-23T16:36:06Z)
• LQP: The Dynamic Logic of Quantum Information [77.34726150561087]
  This paper introduces a dynamic logic formalism for reasoning about information flow in composite quantum systems. We present a finitary syntax, a relational semantics and a sound proof system for this logic. As applications, we use our system to give formal correctness for the Teleportation protocol and for a standard Quantum Secret Sharing protocol.
  arXiv  Detail & Related papers  (2021-10-04T12:20:23Z)
• The Logic of Quantum Programs [77.34726150561087]
  We present a logical calculus for reasoning about information flow in quantum programs. In particular we introduce a dynamic logic that is capable of dealing with quantum measurements, unitary evolutions and entanglements in compound quantum systems.
  arXiv  Detail & Related papers  (2021-09-14T16:08:37Z)
• Tracing Information Flow from Open Quantum Systems [52.77024349608834]
  We use photons in a waveguide array to implement a quantum simulation of the coupling of a qubit with a low-dimensional discrete environment. Using the trace distance between quantum states as a measure of information, we analyze different types of information transfer.
  arXiv  Detail & Related papers  (2021-03-22T16:38:31Z)
• Towards correlation self-testing of quantum theory in the adaptive Clauser-Horne-Shimony-Holt game [1.0878040851638]
  Correlation self-testing of a theory addresses the question of whether we can identify the set of correlations realisable in a theory from its performance in a particular information processing task. This is the first step towards a general solution that could rule out all theories in which the set of realisable correlations does not coincide with the quantum set.
  arXiv  Detail & Related papers  (2020-09-10T18:04:13Z)
• Bounding generalized relative entropies: Nonasymptotic quantum speed limits [0.0]
  Information theory has become an increasingly important research field to better understand quantum mechanics. Relative entropy quantifies how difficult is to tell apart two probability distributions, or even two quantum states. We show how this quantity changes under a quantum process.
  arXiv  Detail & Related papers  (2020-08-27T15:37:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.